34,741 research outputs found
On subshift presentations
We consider partitioned graphs, by which we mean finite strongly connected
directed graphs with a partitioned edge set . With additionally given a relation between
the edges in and the edges in , and denoting
the vertex set of the graph by , we speak of an an -graph . From -graphs we construct semigroups (with zero) that we call
-graph semigroups. We describe a method of presenting subshifts
by means of suitably structured labelled directed graphs with vertex set , edge set , and a label
map that asigns to the edges in labels in an -graph
semigroup . We call the presented subshift an -presentation.
We introduce a Property and a Property (c), tof subshifts, and we
introduce a notion of strong instantaneity. Under an assumption on the
structure of the -graphs we show for strongly instantaneous
subshifts with Property and associated semigroup , that Properties and (c) are
necessary and sufficient for the existence of an -presentation, to which the
subshift is topologically conjugate,Comment: 33 page
Primitive prime divisors in the critical orbit of z^d+c
We prove the finiteness of the Zsigmondy set associated to the critical orbit
of f(z) = z^d+c for rational values of c by finding an effective bound on the
size of the set. For non-recurrent critical orbits, the Zsigmondy set is
explicitly computed by utilizing effective dynamical height bounds. In the
general case, we use Thue-style Diophantine approximation methods to bound the
size of the Zsigmondy set when d >2, and complex-analytic methods when d=2.Comment: This version includes numerous typographical changes and expanded
exposition, and a simplified proof of Theorem 6.1. 30 pages, to appear in
International Math Research Notice
\u3ci\u3eCamellia sinensis\u3c/I\u3e constituents: A Review of Oral Cancer Prevention
Historically, Camellia sinensis (tea) is a plant that has been known to contain antioxidants. Antioxidants such as catechins have been demonstrated to be chemopreventive agents. This review aims to summarize recent findings on the anticancer properties of tea, and its constituents. Since tea is taken orally, and one of the easiest entrances into the human body for microbes is through the oral cavity, this review will focus mainly on oral cancer. Through animal and epidemiological studies, the main active ingredient responsible for the anticancer properties of tea has been determined to be the catechin (-)-epigallocatechin gallate (EGCG). Tea constituents were analyzed through the use of HPLC and confirmed by comparison to authentic standards and mass spectrometry. The results obtained from some studies conflicted with earlier notions that tea catechins act as antioxidants, inhibiting cancer cells. They discovered the catechins to have a pro-oxidant effect, generating reactive oxygen species, such as H2O2. Methods of cancer inhibition were also explored, including cell cycle arrest at certain checkpoints and induction of apoptosis, the active process of cell death. Results from a current study were also examined. Anti-viral and anti-bacterial effects of green and white teas were determined using the plaque method and the Kirby-Bauer, disk-diffusion technique. Results indicated the power of whole tea and tea constituents alongside toothpaste and gum. More than 99% inactivation of viruses was obtained in ten minutes using Tom’s of Maine toothpaste with white tea, whereas infusion of tea into chewing gum yielded over 90% inactivation. Furthermore, distinct zones of inhibition were present for toothpastes and gum treated with tea than for the oral agents by themselves. The future of the research was also briefly discussed. Although many studies have shown beneficial properties of Camellia sinensis, much more epidemiological research remains to be conducted in order to observe the effects on human cancer cells
The critical exponent of the Arshon words
Generalizing the results of Thue (for n = 2) and of Klepinin and Sukhanov
(for n = 3), we prove that for all n greater than or equal to 2, the critical
exponent of the Arshon word of order is given by (3n-2)/(2n-2), and this
exponent is attained at position 1.Comment: 11 page
Fertility Rates and Skill Distribution in Razin and Sadka's Migration-Pension Model: A Note
Razin and Sadka (1999) show that unskilled immigration is beneficial to all income and all age groups in society, even if immigrants are net beneficiaries of the welfare system. Among other things, this result rests on the assumptions that immigrants have the same reproduction rate as the native population and that the immigrants' offspring has the same distribution of skills as the natives' offspring. By relaxing these assumptions, we show that the Razin and Sadka result is no longer unambiguous
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